In a blender, combine 1 cup of the corn with the milk and puree until smooth. Add the heavy cream, eggs and egg yolks and blend. Transfer the mixture to a bowl and whisk in the flour, baking powder, salt and the remaining 1/2 cup of corn kernels.

In a large nonstick skillet, melt 1 tablespoon of the butter in 1 tablespoon of the olive oil. Spoon rounded 2 tablespoon-size dollops of batter into the hot skillet and cook over moderately high heat, turning once, until golden, about 5 minutes. Transfer the corn cakes to a rack and keep warm. Repeat to make the remaining corn cakes, using the remaining 1 tablespoon each of butter and olive oil; adjust the heat if necessary. Serve hot.